Local K-theory index theorem conjecture

Let $A$ be an elliptic operator of order zero on $M$. Let $\sigma(A)$ be its symbol, let $[\sigma(A)]\in K_{1}^{loc}(\Psi^{0}(M)/\Psi^{-1}(M))$ be the corresponding local $K$-theory class, let $[\mathbf{R}(A)]\in K_{0}^{loc}(\Psi^{-1}(M))$ be its local analytical index class, and define

$$(T^{K}.\operatorname{Index})(A)=[\sigma(A)],\qquad (A^{K}.\operatorname{Index})(A)=[\mathbf{R}(A)].$$

Local K-theory index theorem conjecture. For any elliptic operator $A$,

$$\partial^{K, loc}(T^{K}.\operatorname{Index})(A)=(A^{K}.\operatorname{Index})(A),$$

or equivalently,

$$\partial^{K, loc}([\sigma(A)])=[\mathbf{R}(A)].$$

This is the proposed index theorem at the local $K$-theory level, identifying the connecting image of the topological index class with the local analytical index class. The supplied text gives no evidence that it has been resolved.